tofuspeedstar
Bosozoku Champion
dumb thread, negged.
1/3 = .333-[infinite]
- Thread starter Dooby
- Start date
Brown_Pride
All Star
I got it from ignorance bruh
For some reason i was thinking addition but was off base. Again i get WHY things are NEGLIGIBLE and ALMOST I still can't arrive at them being the same when you're having to say the part where they are not the same is negligible.
From a practical perspective i see why .9999999999999 = 1.
But from a literal sense, and to use the prior example, if there are 1 million people + 1 in the room, and you say there are 1 million people in the room then you are not accurate you're approximate, albeit VERY near accurate.
If i remember my calculus right if you take this to infinity the number approaches 1 as you go further out but NEVER get's there. We agree that it is 1 because it's so fuggin close that it's agreed on that it is 1.
If we're talking about infinity....
Then the gap between .9999999 => [Infinity] and 1 is infinitely wide no? How can we say infinity is negligible.
?
O.iatlhawksfan
Devoted Joel Embiid hater
I always wondered this
Breh, there's no difference. They are literally the exact same number.
Maybe this will explain it a little better..
Is 0.999 really equal to 1?
Posted on June 4, 2010 by Guillermo Bautista | 8 Comments
Introduction
Yes it is. 0.999 is equal to 1.
Before we begin our discussion, let me make a remark that the symbol in the decimal 0.999 means that the there are infinitely many 9′s, or putting it in plain language, the decimal number has no end.
For non-math persons, you will probably disagree with the equality, but there are many elementary proofs that could show it, some of which, I have shown below. A proof is a series of valid, logical and relevant arguments (see Introduction to Mathematical Proofs for details), that shows the truth or falsity of a statement.
Proof 1
1/3 = 0.333...
2/3 = 0.666...
1/3 + 2/3 = 0.333... + 0.666...
3/3 = 0.999...
But 3/3 = 1, therefore 1 =0.999...
Proof 2
1/9 = 0.111...
Multiplying both sides by 9 we have
1 = 0.999...
Proof 3
Let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.9999...
9x = 9
x = 1
Hence, 0.999 = 1
Still in doubt?
Many will probably be reluctant in accepting the equality 1 = 0.999... because the representation is a bit counterintuitive. The said equality requires the notion of the real number system, a good grasp of the concept of limits, and knowledge on infinitesimals or calculus in general. If, for instance,you have already taken sequences (in calculus), you may think of the 0.999... as a sequence of real numbers (0.9, 0.99, 0.999, ...). Note that the sequence gets closer and closer to 1, and therefore, its limit is 1.
Is 0.999
Brown_Pride
All Star
so let me say this gain.
i'm not arguing it. I know it. I can do the proofs. The question though is one of semantics.
1/3 <> .3333333333333333333333...
we use .33333333333 as a representation of 1/3. .33333... is not 1/3.
1/3 is a concrete idea. It is 1/3. and we can easily see that 1/3 x 3 = 1.
the idea of Limits, as i understand them and believe you me i'm no expert, is that a certain equation CANNOT reach that number but it comes infinitely close but will never actually reach the limit right? We and by we i mean math and science agree that it IS 1 and as far as infinity goes it's such a negligible amount that we say .9999999.....=1
Even on the graph below those two equations will NEVER intersect, in an extreme literal interpretation of the two equations.
OP is right in a way. The correct statement is that 1 is an APPROXIMATION OF .9999..... because as .999.... approaches infinity, it gets closer to 1, or in other words 1 is the limit of .999999..... 1 is not equal to .99999.... It is an approximation for us in order to do our calculations. Pi is a real number. pi is not equal to 3.14, 3.1415, or 3.1415927, all 3 are approximations for our purposes.
Actually, this is a dope thread IMHO. Too many things are taking for granted without people really understanding it. No such person trying to increase their knowledge can be considered stupid, and in fact, quest for knowledge is a form of intelligence, because the wise man knows he doesn't know everything, and seeks more knowledge from those who have it.
Brown_Pride
All Star
and that's all i'm saying.
IN an extreme literal reading of 999999...... we say it is one...but it is TECHNICALLY not.
The next idea as i've stated is that since there will always be a point between 1 and .9999999.... then the distance between the two numbers is infinite.
1/.999999..... = almost 1, but for sure between 1 and .9999999....
Also, note that infinity is also an approximation for our purposes. At some point, in REALITY, .999999 does reach one, but for OUR purposes, we say it never does. For a mosquito, 10 years might as well be infinity. All these approximations are within a frame of reference. If you are talking about subatomic particles, you can't use these approximations, because even to the fifteenth decimal, those numbers are very important. But if measuring gravitational pull between a few large bodies of mass, such as planets, then yeah, it won't kill you to be a hundredth of a decimal off. So to make it simple, the distance between the two numbers is not infinite, it's infinite relative to our frame of reference.
Brown_Pride
All Star
it's just something where you gotta throw your common sense in the bushes and rely on the math
lol
sounds like religion
jk. Crazy when you really start looking past "what's accepted" and really look at what you're asked to take as a truth. Again, i know it's 1, i just also know it's not.
Ezus Jezus
Ezus Shuttlesworth
1/3 + 1/3 + 1/3 = 1 how?
Shouldn't 3/3 be .999 [infinte]?
this is actually one of the proofs as to why .999999999...=1
EDIT: Damn nvm I read the rest of the thread and I see other nikkas have already addressed this.
VerbalIntercourse
Banned
There is calculus and algebra in Accounting. It's just hidden. Diluted Earnings per share calculations have a hidden global Max/min problem that's easily solved by calculus. of course, it's not presented that way in the class.
statement of cash flows, plug journal entries, discounted/premium bonds, process costing, Completion of contract method, Deferred taxes--these are all accounting methods that require algebra. it just isn't presented that way.
Accounting classes use Tables for the annuity formula, and I think everyone learns about geometric sequences in 7th grade! It's not that accounting is dumbed down. It's that the CPA exam doesn't allow the use annuity formula and you must use tables. The CPA exam also requires the ridiculously archaic "high-low" method for regression lines.
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As for the OP's topic.
I think some people in this thread need to back away from the calculators and just do some long-division by hand.
divide 1 by 3 and you're left with .01 remainder. Divide that by 3 and you're left with another .01 remainder. It's just goes on and on and on, and it never stops. I don't think it is really hard to conceptualize what's happening. that is what infinity is! it's like a pattern that goes on forever and will never end. 1/3 is a Number. Think of it that way. It's a number that get's confusing when it is represented as a decimal. You understand that you can divide a pie into equal three part right?
It's like F(x)= 3/X. Y approaches Infinity as X approaches 0. But X can never be zero. You have to imagine that there is no limit to how fractionally small a quantity can be. X can be .0(insert 1 trillion times 1 trillion zeros)1, but it wouldn't be zero.
It's better to understand that .99999.... = 1 by using limits and not algebra.
Boogaloo Shrimp
Rookie
bunch of smart dumb nikkas in this thread
